Similarity theory and scaling laws for low-temperature plasma discharges: a comprehensive review

Similarity theory and scaling laws determine how physical laws remain the same when control parameters are changed, which is essential for the correlation, prediction, and optimization of discharge plasma parameters under varied conditions. Over the past hundred years, similarity and scaling methods have been broadly explored for low-temperature plasma discharges driven by direct current, alternating current, and pulsed power supplies. Combining scaling laws with similarity theory can greatly reduce the complexity of designing and optimizing plasma devices, especially for geometrically similar discharges of different dimensional scales. This approach further allows extrapolation of plasma discharges to novel parameter regimes without solving equations or conducting experiments. In this review, the establishment and historical development of similarity laws are revisited, and the theoretical interpretation and derivation of similarity theory for different plasma regimes are presented. The similarity properties are demonstrated for various discharge types, including glow discharges, pulsed discharges, streamers, radio-frequency discharges, and microdischarges. The similarity results for plasma discharges from experimental diagnostics, numerical simulations, and theoretical analysis are summarized, and the state-of-the-art progress in the breakdown scaling and dynamical similarities is discussed. Violation mechanisms of the similarity laws, such as nonlinear collision processes, are also elaborated. Finally, the applications, limitations, and future development of similarity theory and scaling laws are discussed.